The following data were collected for the dimerization of ClO to Cl2 O2 at 298 K. [ClO]

step 1 There's a whole lot that's hidden in this question. Okay, so if we take the data that's given to

The following data were collected for the dimerization of...

The following data were collected for the dimerization of $\mathrm{ClO}$ to $\mathrm{Cl}_{2} \mathrm{O}_{2}$ at $298 \mathrm{K}.$ $$\begin{array}{cc} & {[\mathrm{ClO}]} \\ \text { Time (s) } & \text { (molecules/cm }^{3} \text { ) } \\ 0.0 & 2.60 \times 10^{11} \\ \hline 1.0 & 1.08 \times 10^{11} \\ \hline 2.0 & 6.83 \times 10^{10} \\ \hline 3.0 & 4.99 \times 10^{10} \\ \hline 4.0 & 3.93 \times 10^{10} \\ \hline 5.0 & 3.24 \times 10^{10} \\ \hline 6.0 & 2.76 \times 10^{10} \\ \hline \end{array}$$Plot $[\mathrm{ClO}]$ and $\left[\mathrm{Cl}_{2} \mathrm{O}_{2}\right]$ as a function of time and determine the instantancous rates of change in both at 1 s.

The following data were collected for the dimerization of $\mathrm{ClO}$ to $\mathrm{Cl}_{2} \mathrm{O}_{2}$ at $298 \mathrm{K}.$
$$\begin{array}{cc}
& {[\mathrm{ClO}]} \\
\text { Time (s) } & \text { (molecules/cm }^{3} \text { ) } \\
0.0 & 2.60 \times 10^{11} \\
\hline 1.0 & 1.08 \times 10^{11} \\
\hline 2.0 & 6.83 \times 10^{10} \\
\hline 3.0 & 4.99 \times 10^{10} \\
\hline 4.0 & 3.93 \times 10^{10} \\
\hline 5.0 & 3.24 \times 10^{10} \\
\hline 6.0 & 2.76 \times 10^{10} \\
\hline
\end{array}$$Plot $[\mathrm{ClO}]$ and $\left[\mathrm{Cl}_{2} \mathrm{O}_{2}\right]$ as a function of time and determine the instantancous rates of change in both at 1 s.

Key Concepts

Reaction Kinetics

This area of chemistry is concerned with studying the rates at which chemical reactions occur and the factors that affect these rates. It involves understanding how reactant concentrations change with time, the mechanisms by which reactions progress, and the mathematical models that describe these changes.

Instantaneous Rate of Reaction

The instantaneous rate is defined as the derivative of concentration with respect to time at a particular moment. It gives the speed of a reaction exactly at that time point, which is useful for understanding dynamic changes in the system and for comparing reaction speeds under different conditions.

Graphical Analysis of Kinetic Data

Plotting concentration versus time is a key method for visualizing reaction progress. The slope of the tangent line to the curve at any given point represents the instantaneous rate of change of concentration at that moment. This approach allows for a clear interpretation of kinetic data and supports the use of mathematical techniques to extract precise rate values.

Dimerization Reaction Mechanism

A dimerization reaction involves the combination of two identical molecules to form a dimer. Understanding these types of reactions is important in kinetics as they feature a unique reaction pathway and stoichiometry, influencing how the rate law is formulated and how the concentrations of reactants and products are interrelated over time.

Transcript

00:01 There's a whole lot that's hidden in this question.

00:03 Okay, so if we take the data that's given to us and we plot it, at zero seconds, we've got 2 .6 times 10 to the 11, and then we go to 1 .08 times 10 to 11 and so forth.

00:16 We plot the data that's given to us.

00:20 Then we can draw a tangent, and from that tangent, we can assume a slope, change in concentration over change in time.

00:30 You use graph paper, you probably get a little bit better.

00:33 I'm getting about negative 6 .0 times 10 to the 10, not negative 10, times 10 to the 10 molecules per centimeter cubed per second.

00:54 Okay, now the next one is the challenging part.

00:59 It's helpful to write the chemical reaction.

01:02 We recognize that two clos are creating one cl2 -o2.

01:08 So we are producing cl202 at half the rate that we are consuming clo.

01:16 So if we want to determine the rate, instantaneous rate of production of clo2 at one second, then it's just a piece of cake.

01:24 It's just half of that.

01:27 It's half of this.

01:28 It's going to be about three.

01:31 I think your book shows about four times 10 to the 10 molecules.

01:41 Per centimeter cubed per second.

01:44 It's going to be positive because we're making it.

01:47 So how in the world can we graph this? it didn't give us the results for this.

01:52 But what we can do is we can determine the concentrations of cl2o2 at each time by taking the concentrations of clo, their differences...

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